1. Card games and board games have long been a favorite pastime for adults and children alike. Not only are they entertaining, but they also provide the players with the opportunity to get together, to interact in fun and fellowship.
Most of the card games currently available on the market, however, rely primarily on pure chance such as the outcome of tossing a die or of drawing a card from a shuffled deck. The players generally are bound by these outcomes and cannot use their mental ability to exert any control over the pay-offs associated with these random outcomes.
Also, most of the card games currently available are not designed to improve the players' quantitative skills, especially skills in understanding and utilizing probabilities in daily decisions.
Finally, most of the existing card games require the players to retain their cards, and to play only when the time is appropriate. This poorly reflects what happens in real life, where, faced with many decision alternatives, a person normally has to choose one and forgo the rest. For example, because of limited resources and time, a student must decide to study either medicine or law, not medicine then law, nor medicine and law.
2. Decision theory is a well established branch of applied mathematics. In its simplest form, it presents to a decision maker:
(i) a set of decision alternatives, from which he or she must choose one decision;
(ii) a set of states of nature, which are the future random events over which he or she has no control; and
(iii) a rule rewarding to said decision maker with a pay-off, depending o which decision is chosen and which state of nature occurs.
Decision theory provides a method for obtaining the most optimal decision.
For example, early each year, a farmer must decide whether to grow peas (decision d1) or asparagus (decision d2). The states of nature consist of the types of weather which might occur during the year; i.e., perfect weather (state s1), variable weather (state s2) or bad weather (state s3). The farmer has no control over the types of weather. The pay-offs, in terms of thousands of dollars, can be determined as in the following hypothetical table:
TABLE 1 ______________________________________ s1 s2 s3 ______________________________________ d1 4 5 8 d2 2 3 12 ______________________________________
Decision theory represents a serious attempt by scientists to model the "real" world. It is taught at any reputable university-level business school to train students in the art of applying quantitative approaches to decision making. In its simplest form, it can be found in any introductory textbook in Management Science
A related field of study is game theory in which there is a conflict between two or more people. Here, the states of nature are not random events but are determined by the other players. In other words, in game theory, a player does not play against any odds as in decision theory, but against his or her best opponents. Poker, tic-tac-toe and chess are of the type studied in game theory; roulette or craps are not.
Game theory is not concerned with inventing any new game rules, but rather analyzes the behavior of a set of players in an existing game. Thus card games found in game theory literature are normally trivial, having no entertainment or commercial value, and are mainly used to demonstrate the game theory concept. One such game, as an example of the two-person, zero-sum game, can be "Two players each has two cards, a "1" or a 37 2". Unknown to his or her opponent, each player selects one card. The selected cards are then compared. If the sum of the numbers on the cards is even, then one player wins that sum from the other player; if odd, then the latter wins from the former."
It is said that mathematician von Neumann developed game theory to study some form of human behavior and economic phenomena after observing the behavior of poker players. The direction of development here is from game to life, not from theory to game.
Similarly, to the best of my knowledge, no card game which is sold commercially as a concrete form of entertainment has been originated from decision theory. As in game theory, whenever the term "game" is used in the decision theory literature, it has a different connotation. (For example, LaValle, I. H., Fundamentals of Decision Analysis, Holt, Rinehart and Wilston, 1978, pp.14-15) Even if, with a very slim chance, a game similar the present invention has been discussed somewhere in decision theory literature, it could only have been used to demonstrate some basic concept of the theory or to provide a generic model for discussion. Again, because of its orientation towards serious real life applications, it is unobvious for its author and readers to realize its potential as a gaming apparatus or a method of entertainment